Tables And Shares

What are multiplication tables? Multiplication tables list the results (products) of multiplying a whole number by other whole numbers. They help us quickly find answers for repeated addition (for example, 4 + 4 + 4 = 12 is the same as 3 × 4 = 12).

How to read a table entry: In the table, a × b means 'a groups of b' or 'b added a times'. For example, 3 × 5 = 15 means three groups of five items each, giving a total of fifteen items.

Ways to understand and learn tables:

• Repeated addition: 5 × 4 = 5 + 5 + 5 + 5.
• Arrays: Arrange objects in rows and columns (3 rows of 4 makes a 3 × 4 array of 12 dots).
• Number line: Make equal jumps of size b, a times, to reach a × b.
• Skip counting: Count by the number you are multiplying (count by 2s, 3s, 4s, ...).
• Use the commutative property: a × b = b × a (so you only need to memorize up to 10 or 12 in one direction).

Patterns and tricks for quick recall:

• Table of 1: all numbers stay the same. (1 × n = n)
• Table of 2: even numbers only; same as doubling.
• Table of 5: ends in 0 or 5.
• Table of 10: just add a zero at the end.
• Table of 9: use patterns (for 9 × n, digits often add up to 9 for n from 1 to 9).

Multiplication tables up to 10 or 12 are commonly learned in Class 4 to build speed and confidence for solving problems involving shares, arrays and larger multiplications.

What is Skip Counting? Skip counting means counting forward (or backward) by the same number each time instead of by 1. For example, skip counting by 2 gives 2, 4, 6, 8…; skip counting by 5 gives 5, 10, 15, 20…

Why it is useful: Skip counting helps children learn multiplication tables, recognise number patterns, count objects quickly, and solve sharing or grouping problems.

How to do it (step-by-step):

• Choose the step size (the number you will add each time) — this is often called the 'count-by' number (2, 3, 4, 5, 10, etc.).
• Start from the first number (0 or the chosen start like 2 or 3).
• Add the step size repeatedly: start + step, (start + step) + step, and so on.

Connection with Tables: Skip counting by a number is the same as listing the multiples of that number. For example, skip counting by 4 (4, 8, 12, 16…) is the 4 times table (4×1, 4×2, 4×3, 4×4…).

Patterns in skip counting:

• Repeating pattern: Look at the last digits when you skip count by 5: 5, 0, 5, 0… (alternating pattern).
• Even/odd pattern: Skip counting by 2 always gives even numbers (2, 4, 6…).
• Increasing arithmetic pattern: Each term increases by the same amount (the step size).

How to spot patterns quickly: Use a hundred-chart (100-square), number line, or dot arrays to highlight every kth number — patterns like columns, diagonals or repeating end digits become easy to see.

What is Equal Sharing? Equal sharing means dividing objects into equal parts so that each person or group gets the same number. In mathematics this idea is the basis of division. When we share 12 candies among 4 children equally, each child gets the same number of candies. That is division as sharing.

How to think about it

• Start with a total number of objects (the dividend).
• Decide how many people or groups will share them (the divisor).
• Give one object to each person, again and again, until you can’t give everyone another one without running out.
• The number each person has at the end is the quotient. Any leftover objects are the remainder.

Connection with Multiplication and Repeated Subtraction

• If a ÷ b = c, then b × c = a (when there is no remainder). Division reverses multiplication.
• Division as sharing is also repeated subtraction: keep subtracting groups of size b from a until nothing (or less than b) remains; the number of subtractions = quotient.

Key ideas for Class 4 students

• Equal piles: Show objects arranged in piles so each pile has the same number.
• Remainder: If objects can’t be shared equally, leftover objects are called the remainder.
• Words used: share, equally, each, left over, remainder, groups, piles.

Step-by-step example (method to teach)

1. Count the total objects (e.g., 13 sweets).
2. Decide how many people (e.g., 4 children).
3. Give 1 sweet to each child until sweets are fewer than 4.
4. Stop: each child has 3 sweets and 1 sweet remains (13 ÷ 4 = 3 remainder 1).

Using small objects (counters, coins, paper clips) or drawings helps students see equality and remainder clearly.

What is Grouping?
Grouping is a way of doing division where we make equal groups of a given size and find how many such groups we can form. It answers the question: "How many groups of (size) can we make from the total?"

How it works (step-by-step)

• Start with a total number of objects (the dividend).
• Choose the size of each group (the divisor).
• Make equal groups of that size repeatedly (this is repeated subtraction) until you cannot make another full group.
• The number of full groups you have made is the quotient. Any leftover objects that cannot form a full group are the remainder.

Relation to other ideas
Grouping is one view of division. Another view is sharing (where you split the total into a given number of groups and find how many are in each). Both use the same division facts but answer different questions.

Checking your answer
Multiply the divisor (group size) by the quotient (number of groups). Add any remainder. The result should equal the original total.

What are division facts from tables? Division facts from tables are division statements we can get using multiplication tables. Because division is the inverse operation of multiplication, any product in a multiplication table gives one or two easy division facts.

Parts of a division statement: In dividend ÷ divisor = quotient, the dividend is the number being divided, the divisor is the number we divide by, and the quotient is the result. If the dividend is not exactly divisible, there will be a remainder.

How to use a multiplication table to get division facts (step-by-step):b

1. Look at a multiplication table (for 2–10) and pick a product, for example 6 × 4 = 24.
2. From that product you can write the division facts: 24 ÷ 6 = 4 and 24 ÷ 4 = 6.
3. If a number doesn't appear exactly in the table for a divisor, division will give a remainder.

Why this works: A × B = C means C has been made by grouping A items B times (or B items A times). So if we have C items and group them into groups of size A, the number of groups will be B — that is C ÷ A = B.

Tips for Class 4 students: Memorise small multiplication tables (2–10). Use them to quickly find quotients. Always check whether the dividend appears exactly in the chosen divisor’s table to know if there is a remainder.

What the topic means

Word Problems on Tables and Shares combine two simple ideas taught in Class 4: using multiplication tables (repeated addition or equal groups) and sharing (division or equal distribution). In these problems you read a short story, decide whether to multiply (make equal groups) or divide (share equally), form a simple number sentence, solve it and check the answer.

How to solve such problems — step by step

1. Read carefully: underline numbers and what is asked.
2. Decide the operation: if the problem talks about ‘each’, ‘rows’, or ‘groups’ use multiplication (use tables). If it talks about ‘share equally’, ‘how many each’ or ‘how many groups can be made’ use division (sharing or grouping).
3. Write a number sentence: e.g. 7 × 8 = ? or 24 ÷ 6 = ?
4. Use tables or repeated addition to find the product, or use fair sharing/short division to find the quotient.
5. Check with the inverse operation: if you multiplied, check by dividing; if you divided, check by multiplying.

Tips for young learners

• Memorize basic multiplication tables (2 to 10) — they make solving faster.
• Draw pictures: rows of objects for multiplication; circles with objects inside for sharing.
• If there is a remainder when sharing, name it (leftover) and state what to do with it (keep it, distribute later, etc.).

What it means: Using tables means using multiplication tables (like 2, 3, 4, …) to do everyday calculations quickly. Instead of adding the same number many times, we use the table (multiplication) to get the answer fast.

How it helps:

• Turns repeated addition into one multiplication step (e.g., 6 + 6 + 6 + 6 = 6 × 4).
• Makes sharing (division) easier because division is the opposite of multiplication (e.g., if 5 × 4 = 20, then 20 ÷ 5 = 4).
• Useful for counting objects in rows and columns, finding total cost, packing items, and sharing equally.

Simple method to use tables:

1. Recognize the repeated addition or equal groups in the problem.
2. Match it to a multiplication fact from a table (e.g., groups of 7, 8, etc.).
3. If you need sharing, use the related division fact to find how many each gets.

Tips for children:

• Use the commutative property: a × b = b × a. If you don’t know 7 × 4, check 4 × 7.
• Use skip-counting (2, 4, 6, 8...) to find answers on the number line or by counting on fingers/marks.
• Draw arrays (rows and columns) to see the groups visually.

Example problems explained in steps:

• Rows and columns: 5 rows of 6 chairs = 5 × 6 = 30 chairs (use 5th row of table of 6 or array 5×6).
• Buying items: If 1 pen costs ₹8, then 7 pens cost 7 × 8 = ₹56 (use table of 8 or repeated addition 8+8+...).
• Sharing: 24 sweets shared equally by 6 children: 24 ÷ 6 = 4 sweets each (because 6 × 4 = 24).

What this topic means
In Tables and Shares we use multiplication tables to make counting faster and use sharing to divide things equally. Properties are rules about how multiplication and division work. Strategies are easy methods (ways) to use those rules and tables to solve problems quickly.

Key properties (simple rules)

• Commutative property of multiplication: a × b = b × a. Example: 4 × 3 = 3 × 4 = 12.
• Zero and identity properties: 0 × a = 0 and 1 × a = a.
• Distributive property (useful strategy): a × (b + c) = a × b + a × c. This helps split hard multiplications into easier parts. Example: 6 × 7 = 6 × (5 + 2) = 30 + 12 = 42.
• Inverse relation of multiplication and division: If a × b = c, then c ÷ b = a and c ÷ a = b. This links tables to sharing.

Useful strategies

• Skip counting: Count by a number using its table (e.g., 5, 10, 15, 20 for 5s).
• Make groups or arrays: Draw rows and columns (array) to see repeated addition as multiplication (3 rows of 4 = 3 × 4).
• Use known tables to get unknown: If you know 3s and 2s, you can get 6s (2 × 3s) or use doubling and halving.
• Distribute numbers: Break one factor into parts (5 + 2, 10 + 3) and multiply each, then add results.
• Equal sharing and grouping for division: Share objects one by one (equal sharing) or make equal groups (grouping) to divide.
• Number line and repeated subtraction: Use a number line to jump backwards when dividing or to show repeated addition for multiplication.

Using these properties and strategies helps children solve problems faster, check answers, and understand why tables and sharing work.